Problem: The grades on a language midterm at Springer are normally distributed with $\mu = 84$ and $\sigma = 5.0$. Michael earned a $75$ on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Michael's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{75 - {84}}{{5.0}}} $ ${ z \approx -1.80}$ The z-score is $-1.80$. In other words, Michael's score was $1.80$ standard deviations below the mean.